Ventura, Jade
Assistant Professor
Research Interests
Differential geometry. Geometric models of (a) fundamental physical interactions (e.g. general relativity, standard model); (b) life and evolution; (c) consciousness and intelligence.
Differential geometry. Geometric models of (a) fundamental physical interactions (e.g. general relativity, standard model); (b) life and evolution; (c) consciousness and intelligence.
Academic Groups
- Groups, Geometry, and Representations (member)
- Modelling and Applications (affiliate)
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Education
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PhD Mathematics (2021)
Université de Bretagne OccidentaleDissertation: Biconformal Deformations and Solutions to the Einstein Equation
Adviser: Dr. Paul Baird -
MS Mathematics (2014)
University of the Philippines DilimanThesis: Parallel Travel on Spacetime Manifolds
Adviser: Dr. Richard S. Lemence -
BS Applied Mathematics (2010), class valedictorian
University of the Philippines MindanaoThesis: Behavior Pattern Discovery Using Behavior Matrices and Behavior Prediction Relationships: The Case of Prey Delivery Instances of the Philippine Eagle Pithecophaga jefferyi
Adviser: Dr. May Anne E. Mata
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PhD Mathematics (2021)
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Research
Current research projects
- $SU(5)$-bundles
Collaborator: Dr. Clarisson Rizzie Canlubo - Combinatorial universe
Collaborators: Dr. Paul Baird, Dr. Clarisson Rizzie Canlubo - Biconformal deformation: Partial differential equations
Collaborator: Dr. Mark Philip Ona - Biconformal deformation: Riemannian case
Collaborator: Dr. Paul Baird - Biconformal deformation: Space-time case
Collaborators: Dr. Paul Baird, Dr. Jean-Philippe Nicolas - Heuristic optimization on manifolds
Collaborator: Dr. Arrianne Crystal Velasco - Pattern recognition using binary matrices
Collaborators: Dr. May Anne Mata, Dr. Arrianne Crystal Velasco, Ms. Kim Dianne Ligue - Parallel travel on space-times
- Twistor theory on curved manifolds
Collaborator: Dr. Paul Baird
Research students
- Mark Alegre (ongoing)
Topic: Knot theory and Khovanov cohomology
Co-supervisor: Dr. Julius Basilla - Garry Dacillo (ongoing)
Topic: Braided ribbons and quantum codes
Co-supervisor: Dr. Clarisson Rizzie Canlubo - Angelo Emmanuel Ho (ongoing)
Topic: Evolution of shape operator - Alaina Rose Plaza (ongoing)
Topic: Pattern recognition using binary matrices, applied to macaque behavior
Co-supervisors: Dr. May Anne Mata, Ms. Kim Dianne Ligue - Cedie Reyes (ongoing)
- $SU(5)$-bundles
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Teaching
Courses handled/being handled
- Undergraduate courses
Math 20 (or equivalent) Pre-calculus
Math 21 (or equivalent) Calculus 1
Math 22 (or equivalent) Calculus 2
Math 23 (or equivalent) Calculus 3
Math 140 Introduction to modern geometries
Math 146 Differential geometry of curves and surfaces - Graduate courses
Math 246 Differential geometry
- Undergraduate courses
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Publications
- P. Baird and J. Ventura, Four-dimensional Einstein metrics from biconformal deformations, Arch. Math. 57 (2021), no. 5, 255-283, DOI 10.5817/AM2021-5-255.